Subgroups — #44446557

Order 29748.

24 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#21418335	C₂	1	1	yes	maximal, characteristic
2	C₃₇×Dic₆₇	C₃	1	1	yes	maximal, characteristic, complemented, Hall
3	#21418335	C₄	1	1	yes	characteristic, complemented, Hall
4	C₂×C₃₇×C₆₇	C₂×C₃	1	1	yes	characteristic
5	C₃₇×C₆₇	C₃×C₄	1	1	yes	characteristic, complemented, Hall
6	(C₆₇⋊C₃)⋊C₄	—	37	1	no	maximal, Hall
7	C₄×C₃₇⋊C₃	—	67	1	no	maximal, Hall
8	C₂×C₆₇⋊C₃	—	37	1	no	—
9	Dic₆₇	C₃₇⋊C₃	1	1	yes	characteristic, complemented, Hall
10	C₂×C₃₇⋊C₃	—	134	1	no	—
11	C₆₇⋊C₃	—	37	1	no	Hall
12	C₄×C₃₇	—	67	1	no	Hall
13	C₂×C₆₇	C₂×C₃₇⋊C₃	1	1	yes	characteristic
14	C₃₇⋊C₃	—	134	1	no	Hall
15	C₂×C₃₇	D₆₇⋊C₃	1	1	yes	characteristic
16	C₆₇	C₄×C₃₇⋊C₃	1	1	yes	characteristic, complemented, Sylow
17	C₃₇	(C₆₇⋊C₃)⋊C₄	1	1	yes	characteristic, complemented, Sylow
18	C₃×C₄	—	2479	1	no	Hall
19	C₂×C₃	—	4958	1	no	—
20	C₄	—	67	1	no	Sylow
21	C₃	—	4958	1	no	Sylow
22	C₂	#28415606	1	1	yes	characteristic

	subgroup	G/H
center, Frattini, hypercenter	C₂	#28415606
commutator, hypocenter	C₃₇×C₆₇	C₃×C₄
Fitting, socle, cosocle	C₂×C₃₇×C₆₇	C₂×C₃
prime radical	C₂×#21418335	C₂
LCS	G ▷ C₃₇×C₆₇
UCS	C₁ ◁ C₂

Splittings G = N ⋊ H with N normal; H ≅ G/N.

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.